Solve for $x$ and $y$ using elimination. ${-2x-y = -10}$ ${-3x+3y = 3}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $3$ ${-6x-3y = -30}$ $-3x+3y = 3$ Add the top and bottom equations together. $-9x = -27$ $\dfrac{-9x}{{-9}} = \dfrac{-27}{{-9}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {-2x-y = -10}\thinspace$ to find $y$ ${-2}{(3)}{ - y = -10}$ $-6-y = -10$ $-6{+6} - y = -10{+6}$ $-y = -4$ $\dfrac{-y}{{-1}} = \dfrac{-4}{{-1}}$ ${y = 4}$ You can also plug ${x = 3}$ into $\thinspace {-3x+3y = 3}\thinspace$ and get the same answer for $y$ : ${-3}{(3)}{ + 3y = 3}$ ${y = 4}$